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      <a href="/2017/07/16/quick-sort/" title="算法导论之js实现--快速排序" itemprop="url">算法导论之js实现--快速排序</a>
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      <a href="https://godbasin.github.io" title="被删">被删</a>
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    <time datetime="2017-07-16T11:25:45.000Z" itemprop="datePublished">2017-07-16</time>
    更新日期:<time datetime="2017-07-16T11:25:50.263Z" itemprop="dateModified">2017-07-16</time>
    
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			<strong class="toc-title">文章目录</strong>
		<ol class="toc"><li class="toc-item toc-level-2"><a class="toc-link" href="#简单快速排序"><span class="toc-number">1.</span> <span class="toc-text">简单快速排序</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#排序问题"><span class="toc-number">1.1.</span> <span class="toc-text">排序问题</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#思路"><span class="toc-number">1.2.</span> <span class="toc-text">思路</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#js基本思路实现"><span class="toc-number">1.3.</span> <span class="toc-text">js基本思路实现</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#验证"><span class="toc-number">1.4.</span> <span class="toc-text">验证</span></a></li></ol></li><li class="toc-item toc-level-2"><a class="toc-link" href="#快速排序"><span class="toc-number">2.</span> <span class="toc-text">快速排序</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#原址排序"><span class="toc-number">2.1.</span> <span class="toc-text">原址排序</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#快速排序思路"><span class="toc-number">2.2.</span> <span class="toc-text">快速排序思路</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#js基本思路实现-1"><span class="toc-number">2.3.</span> <span class="toc-text">js基本思路实现</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#验证-1"><span class="toc-number">2.4.</span> <span class="toc-text">验证</span></a></li></ol></li></ol>
		</div>
		
		<p>快速排序的javascript实现。<br><a id="more"></a></p>
<h2 id="简单快速排序"><a href="#简单快速排序" class="headerlink" title="简单快速排序"></a>简单快速排序</h2><hr>
<h3 id="排序问题"><a href="#排序问题" class="headerlink" title="排序问题"></a>排序问题</h3><ul>
<li>输入：n个数的一个序列<code>&lt;a1, a2, ..., an&gt;</code></li>
<li>输出：输入序列的一个排列<code>&lt;a1&#39;, a2&#39;, ..., an&#39;&gt;</code>，满足<code>a1&#39; &lt;= a2&#39; &lt;= ... &lt;= an&#39;</code></li>
</ul>
<h3 id="思路"><a href="#思路" class="headerlink" title="思路"></a>思路</h3><p>快速排序使用分治法（Divide and conquer）策略来把一个序列（list）分为两个子序列（sub-lists）。</p>
<p>步骤为：</p>
<ol>
<li>从数列中挑出一个元素，称为”基准”（pivot），</li>
<li>重新排序数列，所有元素比基准值小的摆放在基准前面，所有元素比基准值大的摆在基准的后面（相同的数可以到任一边）。在这个分区结束之后，该基准就处于数列的中间位置。这个称为分区（partition）操作。</li>
<li>递归地（recursive）把小于基准值元素的子数列和大于基准值元素的子数列排序。</li>
</ol>
<p>递归的最底部情形，是数列的大小是零或一，也就是永远都已经被排序好了。虽然一直递归下去，但是这个算法总会结束，因为在每次的迭代（iteration）中，它至少会把一个元素摆到它最后的位置去。</p>
<h3 id="js基本思路实现"><a href="#js基本思路实现" class="headerlink" title="js基本思路实现"></a>js基本思路实现</h3><p>这里我们先使用两个数组分别保存“基准”左边、右边的子集。</p>
<figure class="highlight javascript"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">function</span> <span class="title">fakeQuickSort</span>(<span class="params">iArr</span>) </span>&#123;</div><div class="line">    <span class="keyword">var</span> n = iArr.length;</div><div class="line">    <span class="comment">// 若只有一个，则返回</span></div><div class="line">    <span class="keyword">if</span> (n &lt;=<span class="number">1</span>) &#123; <span class="keyword">return</span> iArr; &#125;</div><div class="line">    <span class="comment">// 若有多个，则选择基准进行分组，递归处理</span></div><div class="line">    <span class="keyword">else</span>&#123;</div><div class="line">        <span class="keyword">var</span> p = <span class="built_in">parseInt</span>(n<span class="number">-1</span>);</div><div class="line">        <span class="keyword">var</span> pivot = iArr[p];</div><div class="line">        <span class="keyword">var</span> leftArr = [], rightArr = [], arrVal;</div><div class="line">        <span class="keyword">for</span>(<span class="keyword">var</span> i = <span class="number">0</span>; i &lt; n<span class="number">-1</span>; i++)&#123;</div><div class="line">            arrVal = iArr[i];</div><div class="line">            <span class="keyword">if</span>(arrVal &lt;= pivot)&#123;</div><div class="line">                <span class="comment">// 小于基准放置左侧</span></div><div class="line">                leftArr.push(arrVal);</div><div class="line">            &#125;<span class="keyword">else</span>&#123;</div><div class="line">                <span class="comment">// 大于基准放置右侧</span></div><div class="line">                rightArr.push(arrVal);</div><div class="line">            &#125;</div><div class="line">        &#125;</div><div class="line">        <span class="comment">// 递归计算左边、右边子集，将数组合并返回</span></div><div class="line">        <span class="keyword">return</span> fakeQuickSort(leftArr).concat([pivot].concat(fakeQuickSort(rightArr)));</div><div class="line">    &#125;</div><div class="line">&#125;</div></pre></td></tr></table></figure>
<h3 id="验证"><a href="#验证" class="headerlink" title="验证"></a>验证</h3><figure class="highlight javascript"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div></pre></td><td class="code"><pre><div class="line">fakeQuickSort([<span class="number">5</span>, <span class="number">2</span>, <span class="number">4</span>, <span class="number">6</span>, <span class="number">1</span>, <span class="number">3</span>]); </div><div class="line"><span class="comment">// 输出[1, 2, 3, 4, 5, 6]</span></div><div class="line"></div><div class="line">fakeQuickSort([<span class="number">2</span>, <span class="number">1</span>, <span class="number">3</span>, <span class="number">1</span>, <span class="number">5</span>]);</div><div class="line"><span class="comment">// 输出[1, 1, 2, 3, 5]</span></div><div class="line"></div><div class="line">fakeQuickSort([<span class="number">5</span>, <span class="number">2</span>, <span class="number">12</span>, <span class="number">2</span>, <span class="number">134</span>, <span class="number">1</span>, <span class="number">3</span>, <span class="number">34</span>, <span class="number">4</span>, <span class="number">6</span>, <span class="number">1</span>, <span class="number">3</span>, <span class="number">4</span>]); </div><div class="line"><span class="comment">// 输出[1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 12, 34, 134]</span></div></pre></td></tr></table></figure>
<h2 id="快速排序"><a href="#快速排序" class="headerlink" title="快速排序"></a>快速排序</h2><hr>
<h3 id="原址排序"><a href="#原址排序" class="headerlink" title="原址排序"></a>原址排序</h3><p>在排序算法中，如果输入数组中仅有常数个元素需要在排序过程中存储在数组之外，则称排序算法是原址的。</p>
<p>插入排序、堆排序、快速排序等都是原址排序。<br>归并排序不是原址的。</p>
<p>上面简单版本的缺点是，它需要Ω(n)的额外存储空间，也就跟归并排序一样不好。额外需要的存储器空间配置，在实际上的实现，也会极度影响速度和缓存的性能。有一个比较复杂使用原地（in-place）分区算法的版本，且在好的基准选择上，平均可以达到O(log n)空间的使用复杂度。</p>
<h3 id="快速排序思路"><a href="#快速排序思路" class="headerlink" title="快速排序思路"></a>快速排序思路</h3><p>上面我们移动位置是通过建立新的子集数组伪装的，这里我们则需要实现真正的位置交换。</p>
<ul>
<li>获取基准值</li>
<li>将低于基准值的排列在左侧，剩下的排列在右侧</li>
<li>分别对左侧和右侧进行递归排序</li>
</ul>
<p>这是原址排序算法，它分区了标示为”左边（left）”和”右边（right）”的序列部分，借由移动小于a[pivotIndex]的所有元素到子序列的开头，留下所有大于或等于的元素接在他们后面。<br>在这个过程它也为基准元素找寻最后摆放的位置，也就是它回传的值。它暂时地把基准元素移到子序列的结尾，而不会被前述方式影响到。</p>
<p>由于算法只使用交换，因此最后的数列与原先的数列拥有一样的元素。要注意的是，一个元素在到达它的最后位置前，可能会被交换很多次。</p>
<p>参考<a href="https://zh.wikipedia.org/wiki/%E5%BF%AB%E9%80%9F%E6%8E%92%E5%BA%8F" target="_blank" rel="external">快速排序-wiki</a></p>
<h3 id="js基本思路实现-1"><a href="#js基本思路实现-1" class="headerlink" title="js基本思路实现"></a>js基本思路实现</h3><figure class="highlight javascript"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div></pre></td><td class="code"><pre><div class="line"><span class="comment">// 交换数组值</span></div><div class="line"><span class="function"><span class="keyword">function</span> <span class="title">swap</span>(<span class="params">arr, a, b</span>) </span>&#123;</div><div class="line">    <span class="keyword">if</span>(a == b)&#123;<span class="keyword">return</span>;&#125;</div><div class="line">    <span class="keyword">var</span> c = arr[a];</div><div class="line">    arr[a] = arr[b];</div><div class="line">    arr[b] = c;</div><div class="line">&#125;</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">function</span> <span class="title">quickSort</span>(<span class="params">iArr, start, end</span>) </span>&#123;</div><div class="line">    <span class="keyword">var</span> n = end - start;</div><div class="line">    <span class="comment">// 若只有一个或者没有，则返回</span></div><div class="line">    <span class="keyword">if</span> (n &lt;= <span class="number">1</span>) &#123; <span class="keyword">return</span>; &#125;</div><div class="line">    <span class="comment">// 若有多个，则选择基准进行位置调整，递归处理</span></div><div class="line">    <span class="keyword">else</span> &#123;</div><div class="line">        <span class="keyword">var</span> p = end - <span class="number">1</span>; <span class="comment">// 选取最后一个作为基准</span></div><div class="line">        <span class="keyword">var</span> pivot = iArr[p]; <span class="comment">// 获取基准值</span></div><div class="line">        <span class="keyword">var</span> leftIndex = start; <span class="comment">// 记录左侧列表位置</span></div><div class="line">        <span class="keyword">for</span> (<span class="keyword">var</span> i = <span class="number">0</span>; i &lt; n - <span class="number">1</span>; i++) &#123;</div><div class="line">            arrVal = iArr[start + i];</div><div class="line">            <span class="comment">// 若小于基准，则排列在左侧</span></div><div class="line">            <span class="keyword">if</span> (arrVal &lt;= pivot) &#123;</div><div class="line">                swap(iArr, leftIndex++, start + i)</div><div class="line">            &#125;</div><div class="line">            <span class="comment">// 若大于基准，继续</span></div><div class="line">        &#125;</div><div class="line">        <span class="comment">// 交换基准至中间</span></div><div class="line">        swap(iArr, leftIndex, p);</div><div class="line">        <span class="comment">// 递归排序左侧</span></div><div class="line">        quickSort(iArr, start, leftIndex);</div><div class="line">        <span class="comment">// 递归排序右侧</span></div><div class="line">        quickSort(iArr, leftIndex + <span class="number">1</span>, end);</div><div class="line">        <span class="keyword">return</span> iArr;</div><div class="line">    &#125;</div><div class="line">&#125;</div></pre></td></tr></table></figure>
<h3 id="验证-1"><a href="#验证-1" class="headerlink" title="验证"></a>验证</h3><figure class="highlight javascript"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div></pre></td><td class="code"><pre><div class="line">quickSort([<span class="number">5</span>, <span class="number">2</span>, <span class="number">4</span>, <span class="number">6</span>, <span class="number">1</span>, <span class="number">3</span>], <span class="number">0</span>, <span class="number">6</span>); </div><div class="line"><span class="comment">// 输出[1, 2, 3, 4, 5, 6]</span></div><div class="line"></div><div class="line">quickSort([<span class="number">2</span>, <span class="number">1</span>, <span class="number">3</span>, <span class="number">1</span>, <span class="number">5</span>], <span class="number">0</span>, <span class="number">5</span>);</div><div class="line"><span class="comment">// 输出[1, 1, 2, 3, 5]</span></div><div class="line"></div><div class="line">quickSort([<span class="number">5</span>, <span class="number">2</span>, <span class="number">12</span>, <span class="number">2</span>, <span class="number">134</span>, <span class="number">1</span>, <span class="number">3</span>, <span class="number">34</span>, <span class="number">4</span>, <span class="number">6</span>, <span class="number">1</span>, <span class="number">3</span>, <span class="number">4</span>], <span class="number">0</span>, <span class="number">13</span>); </div><div class="line"><span class="comment">// 输出[1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 12, 34, 134]</span></div></pre></td></tr></table></figure>
  
		
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  <ol class="toc"><li class="toc-item toc-level-2"><a class="toc-link" href="#简单快速排序"><span class="toc-number">1.</span> <span class="toc-text">简单快速排序</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#排序问题"><span class="toc-number">1.1.</span> <span class="toc-text">排序问题</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#思路"><span class="toc-number">1.2.</span> <span class="toc-text">思路</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#js基本思路实现"><span class="toc-number">1.3.</span> <span class="toc-text">js基本思路实现</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#验证"><span class="toc-number">1.4.</span> <span class="toc-text">验证</span></a></li></ol></li><li class="toc-item toc-level-2"><a class="toc-link" href="#快速排序"><span class="toc-number">2.</span> <span class="toc-text">快速排序</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#原址排序"><span class="toc-number">2.1.</span> <span class="toc-text">原址排序</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#快速排序思路"><span class="toc-number">2.2.</span> <span class="toc-text">快速排序思路</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#js基本思路实现-1"><span class="toc-number">2.3.</span> <span class="toc-text">js基本思路实现</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#验证-1"><span class="toc-number">2.4.</span> <span class="toc-text">验证</span></a></li></ol></li></ol>
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